Positive solutions of nonlinear third-order boundary value problem with integral boundary conditions

Abstract

In this paper, we study the existence of positive solutions for boundary value problems of third-order two-point differential equations with integral boundary conditions. we mainly use the Krasnoselskii's fixed point theorem Value problem, at least there is a positive solution, and give an example to verify the conclusion.

Solvability for a nonlinear third-order three-point boundary value problem

“…In this way we remove the half of the assumptions to prove the existence of a solution when using Krasnoselskii's fixed point theorem. (See [10,17,19]). Moreover, we establish our results for t in [0, T ].…”

“…Since f ∞ = 0 and from Theorem 3.2, we can get that the (4.1)-(4.2) has at least one positive solution. Consequently, we cannot apply the Krasnoselskii's fixed point theorem like in [10,17,19] Example 4.2. Consider the boundary value problem where α = 15, η = 0, 2 = 1 5 , T = 3 4 , 0 < α = 15 < 37, 5 = 2T…”

“…On the other hand, we have f 0 = 1 , then the function f is not superlinear. Consequently, we cannot apply the Krasnoselskii's fixed point theorem like in [10,17,19]…”

Existence of Multiple Solutions for Second-Order Problem with Stieltjes Integral Boundary Condition

“…In the past few decades, the boundary value problems have appealed to many scholars in the mathematical field. Generally speaking, the boundary value problems mostly involve in two-point [1][2][3][4][5], three-point [6][7][8], and multipoint [9][10][11]. Many physical phenomena were formulated as nonlocal mathematical models with integral boundary conditions [12][13][14][15][16][17][18][19][20][21], such as fractional differential equation [22][23][24][25][26][27][28][29][30], nonlinear singular parabolic equation [31], and general second-order equation [19,[32][33][34][35][36][37][38][39][40].…”

Triple positive solutions for a class of boundary value problems with integral boundary conditions

“…The boundary value problems of higher-order have been examined due to their mathematical importance and applications in different areas of applied sciences. In particular, third-order, fourth-order and nth order were considred, see [3,4,5,6,7,10,11,20,23,27,34] and the references therein.…”